Computed tomography includes the principal fields of transmission computed tomography and emission computed tomography. Additionally, there are at least two distinct geometric systems in either transmission or emission computed tomography. The first is parallel beam geometry in which the source/detector relationship is such that all rays within any particular view are parallel to each other. The second is fan beam geometry in which the source/detector relationship is such that all rays within any view converge to a point. In one form of transmission computed tomography (TCT), an X-ray source and a multi-channel detector are fixed with respect to each other and mounted for rotation on a gantry on opposite sides of a patient aperture. During the course of a scan, a number of projections are taken which are later convolved and back projected to produce a pixelized image representing the linear attenuation coefficients of the slice of the body through which the radiation had passed.
In emission computed tomography (ECT), gamma emitting substances are ingested or injected into the body, following which the body is scanned to detect the concentration and distribution of the radioactive sources by taking projections at a plurality of angles around the body and reconstructing an image from these projections. An example of fan beam emission computed tomography is the rotating gamma camera used with a converging collimator. The collimator is intended to converge at a focal point a fixed distance from the gamma camera.
One of the factors accounted for in true fan beam reconstruction procedures is the diverging nature of the fan beam itself. The normal form of the Radon inversion relationship, on which many reconstruction techniques depend, assumes parallel beam geometry. When fan beam projections are reconstructed, the relationship between the parallel rays and the diverging rays is typically accounted for in or just prior to the convolution operation as well as in the back projection operation which must map the data according to the geometry of the system.
The problem of attenuation is one of the major complicating factors in image reconstruction with emission computed tomography. Among the problems that occur in ECT as a result of attenuation are "hot rim" artifacts and inaccurate data related to perceived asymmetrical organ uptake of injected radionuclides. Attenuation also reduces lesion contrast, and thus the detectability of interior lesions, and in addition, can cause volume deformation which makes it difficult to evaluate lesion size. Therefore, one of the difficulties involved in emission tomographic reconstruction procedures is to determine whether a count reduction is due to reduced perfusion or the ingested gamma emitting substances being attenuated within the body.
The first step in applying most attenuation correction procedures is the determination of the body contour or boundary. Once the boundary is determined, many procedures treat the entire body as having a constant attenuation coefficient. One approach to determining the body contour for reconstruction procedures is to fit the body contour to an ellipse, which is suitable for most cases. This may not be appropriate for all body contours, in which case the boundary may have to be defined by a more general convex boundary or, in a rare and most difficult case, a non-convex boundary.
As described above, most methods currently used obtain the body contour and assume a constant attenuation within the boundary. This is the method described in a paper co-authored by the instant inventor: Gullberg, Malko and Eisner, "Boundary Determination Methods For Attenuation Correction In Single Photon Emission Computed Tomography," Emission Computed Tomography, Society of Nuclear Medicine, pp. 33-53, 1983. In the above paper, a method for determining elliptical parameters which best estimate the body contour is presented but is limited to the field of parallel beam emission computed tomography.
While the method presented in the above paper is useful in the parallel beam geometry case, the estimating technique which is developed applies only to the parallel beam case, and cannot be used for the more general fan beam geometry. It is recognized, however, that in emission CT, fan beam collimators improve sensitivity and resolution over systems using parallel beam collimators. Without a method for determining elliptical parameters that best estimate the body contour when using fan beam collimators, practitioners have been faced with a number of alternatives, all of which have significant disadvantages.
A number of methods for determining the body contour have required multiple scans and are summarized below. A more detailed description may be found in the above mentioned Gullberg et al. paper entitled "Boundary Determination Method For Attenuation Correction In Single Photon Emission Computed Tomography." In these multiple scan techniques, preliminary scans obtain data relating only to the body outline. Further scans, however, are then required for the actual CT reconstructions.
One multiple scan method is the "point source" method. The point source method requires two projections in addition to the projections for the patient study. When the patient is lying supine on the imaging table, either a frontal or anterior view can measure the major axis of the ellipse, and a lateral view can measure the minor axis. For the major axis, a point source is positioned at an appropriate right and left lateral position. The distance between each centroid gives the length of the major axis. Adding together the projection coordinate for each centroid and dividing by two gives the location of one of the coordinates for the center of the ellipse. Likewise placing point sources on the patient anterior and posterior, a lateral view gives the length of the minor axis for the ellipse and the other coordinate for the center of the ellipse.
A second example of multiple scan techniques used to define the body contour when using fan beam reconstruction procedures is the use of an external ring of a gamma emitting source taped to the body. One data set is taken with the external ring source and one data set is taken without. Care must be taken to not move the patient between the two separate studies as the source is manipulated around the patient. The reconstruction of the projections with the ring source gives the body outline bounded by the ring of activity and the attenuation coefficient within the boundary is assumed to be constant.
A method presented in "Boundary Determination Methods For Attenuation Correction In Single Photon Emission Computed Tomography," discussed above, presents an alternative to these multiple scan techniques, but only for parallel beam systems. Specifically, on pages 43-46 of the article, the authors define a set of arbitrary elliptical parameters and present a method for determining the values for the parameters to define an ellipse which most closely represents the body contour. As previously mentioned, the article and method apply only to a parallel beam geometric system. Because of the parallel beam geometry, the method produces two chi-square functions to be optimized to yield the optimal values for the parameters of the ellipse. As noted on page 46, and as a direct consequence of the parallel beam geometry, one of the chi-square functions is simply a linear estimation problem that immediately determines the coordinates for the center of the ellipse. Therefore, two of the five required parameters are immediately apparent, while an iterative procedure is suggested to obtain the other three values.
Because of the diverging nature of the fan beam geometry, the above disclosed procedure cannot be applied to systems employing fan beam geometry. Consequently, in fan beam systems, the practitioner has been left to the multiple scan techniques discussed above. Conceptually, it would be possible to "rebin" the fan beam data into parallel beam data sets and proceed with the parallel beam method described, but as a practical matter that is not believed to have been accomplished because rebinning is inaccurate and introduces significant computational complications.